Gentle Sum

Calculus Level 4

\[ \large \lim_{n\to\infty} \dfrac1{4n^2} \sum_{k=1}^n \sqrt{4n^2-k^2} \]

If the limit above equals to \( \dfrac{\pi}P + \dfrac {\sqrt 3}R \) for positive integers \(P\) and \(R\), find the value of \(P + R\).

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